The observation of massive black hole binaries ( MBHBs ) with Pulsar Timing Arrays ( PTAs ) is one of the goals of gravitational wave astronomy in the coming years .
Massive ( \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 ^ { 8 } M _ { \odot } ) and low-redshift ( \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 1.5 ) sources are expected to be individually resolved by up-coming PTAs , and our ability to use them as astrophysical probes will depend on the accuracy with which their parameters can be measured .
In this paper we estimate the precision of such measurements using the Fisher-information-matrix formalism .
For this initial study we restrict to “ monochromatic ” sources , i.e . binaries whose frequency evolution is negligible during the expected \approx 10 yr observation time , which represent the bulk of the observable population based on current astrophysical predictions .
In this approximation , the system is described by seven parameters and we determine their expected statistical errors as a function of the number of pulsars in the array , the array sky coverage , and the signal-to-noise ratio ( SNR ) of the signal .
At fixed SNR ( regardless of the number of pulsars in the PTA ) , the gravitational wave astronomy capability of a PTA is achieved with \approx 20 pulsars ; adding more pulsars ( up to 1000 ) to the array reduces the source error-box in the sky \Delta \Omega by a factor \approx 5 and has negligible consequences on the statistical errors on the other parameters , because the correlations amongst parameters are already removed to a large extend .
If one folds in the increase of coherent SNR proportional to the square root of the number of pulsars , \Delta \Omega improves as 1 / \mathrm { SNR } ^ { 2 } and the other parameters as 1 / \mathrm { SNR } .
For a fiducial PTA of 100 pulsars uniformly distributed in the sky and a coherent SNR = 10 , we find \Delta \Omega \approx 40 \mathrm { deg } ^ { 2 } , a fractional error on the signal amplitude of \approx 30 \% ( which constraints only very poorly the chirp mass - luminosity distance combination { \cal M } ^ { 5 / 3 } / D _ { L } ) , and the source inclination and polarization angles are recovered at the \approx 0.3 rad level .
The ongoing Parkes PTA is particularly sensitive to systems located in the southern hemisphere , where at SNR = 10 the source position can be determined with \Delta \Omega \approx 10 \mathrm { deg } ^ { 2 } , but has poorer ( by an order or magnitude ) performance for sources in the northern hemisphere .